{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we build the Integers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dataclasses import dataclass\n",
    "from typing import List"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0 Node(1)\n",
      "0 1 Node(1)\n",
      "1 0 Node(1)\n",
      "1 1 Node(0)\n"
     ]
    }
   ],
   "source": [
    "# we start with the holy binary NAND gate (::bow::) (sorry NOR)\n",
    "# NAND is Universal, i.e. we can build any boolean expression out of it alone. Cool right?\n",
    "\n",
    "# bnand = lambda a, b: 0 if a == 1 and b == 1 else 1\n",
    "\n",
    "# nvm let's wrap values into classes so we can trace the graph and create pretty visualizations\n",
    "\n",
    "class Node:\n",
    "    \n",
    "    def __init__(self, bit, prev=None):\n",
    "        self.bit = bit\n",
    "        self._prev = [] if prev is None else prev\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return \"Node(%d)\" % self.bit\n",
    "\n",
    "def bnand(a, b):\n",
    "    \n",
    "    # wrap inputs into Nodes if needed\n",
    "    if isinstance(a, int):\n",
    "        a = Node(a)\n",
    "    if isinstance(b, int):\n",
    "        b = Node(b)\n",
    "\n",
    "    # calculate nand\n",
    "    out_bit = 0 if a.bit == 1 and b.bit == 1 else 1\n",
    "    out = Node(out_bit, [a, b]) # keep pointers to the children of this node\n",
    "    \n",
    "    return out\n",
    "\n",
    "print(0, 0, bnand(0, 0))\n",
    "print(0, 1, bnand(0, 1))\n",
    "print(1, 0, bnand(1, 0))\n",
    "print(1, 1, bnand(1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 Node(1)\n",
      "1 Node(0)\n"
     ]
    }
   ],
   "source": [
    "# binary not\n",
    "bnot = lambda a: bnand(a, a)\n",
    "print(0, bnot(0))\n",
    "print(1, bnot(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0 Node(0)\n",
      "0 1 Node(0)\n",
      "1 0 Node(0)\n",
      "1 1 Node(1)\n"
     ]
    }
   ],
   "source": [
    "# binary and\n",
    "band = lambda a, b: bnot(bnand(a, b))\n",
    "print(0, 0, band(0, 0))\n",
    "print(0, 1, band(0, 1))\n",
    "print(1, 0, band(1, 0))\n",
    "print(1, 1, band(1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0 Node(0)\n",
      "0 1 Node(1)\n",
      "1 0 Node(1)\n",
      "1 1 Node(0)\n"
     ]
    }
   ],
   "source": [
    "# binary xor\n",
    "bxor = lambda a, b: band(bnand(a, b), bnand(bnot(a), bnot(b)))\n",
    "print(0, 0, bxor(0, 0))\n",
    "print(0, 1, bxor(0, 1))\n",
    "print(1, 0, bxor(1, 0))\n",
    "print(1, 1, bxor(1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0 Node(0)\n",
      "0 1 Node(1)\n",
      "1 0 Node(1)\n",
      "1 1 Node(1)\n"
     ]
    }
   ],
   "source": [
    "# binary or\n",
    "bor = lambda a, b: bnot(band(bnot(a), bnot(b)))\n",
    "print(0, 0, bor(0, 0))\n",
    "print(0, 1, bor(0, 1))\n",
    "print(1, 0, bor(1, 0))\n",
    "print(1, 1, bor(1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0 (Node(0), Node(0))\n",
      "0 1 (Node(1), Node(0))\n",
      "1 0 (Node(1), Node(0))\n",
      "1 1 (Node(0), Node(1))\n"
     ]
    }
   ],
   "source": [
    "def half_adder(a, b):\n",
    "    s = bxor(a, b) # sum\n",
    "    c = band(a, b) # carry\n",
    "    return s, c\n",
    "\n",
    "print(0, 0, half_adder(0, 0))\n",
    "print(0, 1, half_adder(0, 1))\n",
    "print(1, 0, half_adder(1, 0))\n",
    "print(1, 1, half_adder(1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0 0 (Node(0), Node(0))\n",
      "0 0 1 (Node(1), Node(0))\n",
      "0 1 0 (Node(1), Node(0))\n",
      "0 1 1 (Node(0), Node(1))\n",
      "1 0 0 (Node(1), Node(0))\n",
      "1 0 1 (Node(0), Node(1))\n",
      "1 1 0 (Node(0), Node(1))\n",
      "1 1 1 (Node(1), Node(1))\n"
     ]
    }
   ],
   "source": [
    "def full_adder(a, b, c): # adds 3 bits by connecting two half_adders in series\n",
    "    s1, c1 = half_adder(a,  b)\n",
    "    s2, c2 = half_adder(s1, c)\n",
    "    return s2, bor(c1, c2)\n",
    "\n",
    "print(0, 0, 0, full_adder(0, 0, 0))\n",
    "print(0, 0, 1, full_adder(0, 0, 1))\n",
    "print(0, 1, 0, full_adder(0, 1, 0))\n",
    "print(0, 1, 1, full_adder(0, 1, 1))\n",
    "print(1, 0, 0, full_adder(1, 0, 0))\n",
    "print(1, 0, 1, full_adder(1, 0, 1))\n",
    "print(1, 1, 0, full_adder(1, 1, 0))\n",
    "print(1, 1, 1, full_adder(1, 1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "@dataclass\n",
    "class UInt:\n",
    "    bits: List[Node]\n",
    "    \n",
    "    def val(self):\n",
    "        # return the python object of the stored integer\n",
    "        u = sum((2**i if d.bit==1 else 0) for i,d in enumerate(self.bits[::-1]))\n",
    "        return u\n",
    "    \n",
    "    def __add__(self, other):\n",
    "        assert len(self.bits) == len(other.bits)\n",
    "        \n",
    "        out = []\n",
    "        c = 0\n",
    "        for a, b in zip(self.bits[::-1], other.bits[::-1]):\n",
    "            s, c = full_adder(a, b, c)\n",
    "            out.append(s)\n",
    "        \n",
    "        # note: final carry gets dropped! such is life in a finite universe\n",
    "        return UInt(out[::-1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0, 0, 0, 0, 1, 1, 0]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def uint_binary(num, nbits=8):\n",
    "    assert 0 <= num < 2**nbits\n",
    "    out = []\n",
    "    for _ in range(nbits):\n",
    "        bit = num %  2\n",
    "        num = num // 2\n",
    "        out.append(bit)\n",
    "    return out[::-1]\n",
    "\n",
    "uint_binary(6, nbits=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "256 OK\n"
     ]
    }
   ],
   "source": [
    "# ok les do verification\n",
    "nbits = 4 # test addition of up to 4-bit integers, so range 0..15\n",
    "nrang = 2**nbits\n",
    "ntests = 0\n",
    "for a in range(nrang):\n",
    "    for b in range(nrang):\n",
    "        a_bits = list(map(Node, uint_binary(a, nbits=nbits)))\n",
    "        b_bits = list(map(Node, uint_binary(b, nbits=nbits)))\n",
    "        s = UInt(a_bits) + UInt(b_bits)\n",
    "        assert ((a + b) % nrang) == s.val()\n",
    "        ntests += 1\n",
    "print(ntests, 'OK')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make up some random addition example\n",
    "a_bits = list(map(Node, uint_binary(103, nbits=8)))\n",
    "b_bits = list(map(Node, uint_binary(79, nbits=8)))\n",
    "s = UInt(a_bits) + UInt(b_bits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Node(0), Node(1), Node(1), Node(0), Node(0), Node(1), Node(1), Node(1)]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_bits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Node(0), Node(1), Node(0), Node(0), Node(1), Node(1), Node(1), Node(1)]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_bits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Node(1), Node(0), Node(1), Node(1), Node(0), Node(1), Node(1), Node(0)]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.bits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "182"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.val()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "182"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "103 + 79"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graphviz import Digraph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trace(root):\n",
    "    nodes, edges = set(), set()\n",
    "    def build(v):\n",
    "        if v not in nodes:\n",
    "            nodes.add(v)\n",
    "            for child in v._prev:\n",
    "                edges.add((child, v))\n",
    "                build(child)\n",
    "    build(root)\n",
    "    return nodes, edges\n",
    "\n",
    "def draw_dot(root, format='svg', rankdir='LR'):\n",
    "    assert rankdir in ['LR', 'TB']\n",
    "    \n",
    "    nodes, edges = set(), set()\n",
    "    for r in root.bits:\n",
    "        ns, es = trace(r)\n",
    "        nodes.update(ns)\n",
    "        edges.update(es)\n",
    "    \n",
    "    print(len(nodes))\n",
    "    dot = Digraph(format=format, graph_attr={'rankdir': rankdir}) #, node_attr={'rankdir': 'TB'})\n",
    "    \n",
    "    for n in nodes:\n",
    "        \n",
    "        if n._prev:\n",
    "            label = \"{ %d NAND %d = %d }\" % (n._prev[0].bit, n._prev[1].bit, n.bit)\n",
    "        else:\n",
    "            label = \"{ %d }\" % (n.bit, )\n",
    "            \n",
    "        dot.node(name=str(id(n)), label=label, shape='record')\n",
    "        \n",
    "    for n1, n2 in edges:\n",
    "        dot.edge(str(id(n1)), str(id(n2)))\n",
    "    \n",
    "    return dot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "179\n"
     ]
    },
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